Comment on ``Renormalization-group picture of the Lifshitz critical behavior''

Abstract

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {\bf 67}, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not give an ultraviolet finite renormalized theory, is plagued by inconsistencies, misses the existence of a nontrivial anisotropy exponent $\theta \ne 1/2$, and therefore yields incorrect hyperscaling relations. His $\epsilon$-expansion results to order ${\epsilon }^2$ for the critical exponents of $m$-axial Lifshitz points are incorrect both in the anisotropic ($0<m<d$) and the isotropic cases ($m=d$). The inherent inconsistencies and the lack of a sound basis of the approach makes its results unacceptable even if they are interpreted in the sense of approximations.

A comment on M. Leite, Phys Rev B 67, 104415 (2003) revtex4, 2 pages

Cited by in corpus (2)

• Large-n expansion for m-axial Lifshitz points
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